Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
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Gaussian r<strong>and</strong>om variables<br />
<strong>Overview</strong> <strong>of</strong><br />
<strong>basic</strong> <strong>concepts</strong><br />
<strong>in</strong> <strong>Statistics</strong><br />
<strong>and</strong><br />
<strong>Probability</strong><br />
Avanti<br />
Athreya<br />
Prelim<strong>in</strong>aries<br />
Important<br />
distributions,<br />
scal<strong>in</strong>g laws,<br />
<strong>and</strong> the CLT<br />
Parametric<br />
estimation <strong>and</strong><br />
hypothesis<br />
test<strong>in</strong>g<br />
A cont<strong>in</strong>uous r<strong>and</strong>om variable is called Gaussian or normal with<br />
parameters µ <strong>and</strong> σ if it has a density given by<br />
f (x) = 1<br />
σ √ (x−µ)2<br />
e− 2σ 2<br />
2π<br />
The expected value <strong>of</strong> X is µ, <strong>and</strong> the st<strong>and</strong>ard deviation<br />
√<br />
V (X) is σ.<br />
If X 1 , · · · ,X n are i.i.d N(µ,σ), then any l<strong>in</strong>ear comb<strong>in</strong>ation<br />
∑ n<br />
1 a iX i is also normal!
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